Question: Solve for $x$ and $y$ using elimination. ${x+2y = 20}$ ${-x+5y = 29}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $7y = 49$ $\dfrac{7y}{{7}} = \dfrac{49}{{7}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {x+2y = 20}\thinspace$ to find $x$ ${x + 2}{(7)}{= 20}$ $x+14 = 20$ $x+14{-14} = 20{-14}$ ${x = 6}$ You can also plug ${y = 7}$ into $\thinspace {-x+5y = 29}\thinspace$ and get the same answer for $x$ : ${-x + 5}{(7)}{= 29}$ ${x = 6}$